Alternate exterior angles are a mathematical concept. They are created when a transversal crosses two lines. The lines crossed are usually parallel. So, if a transversal line a intersects two parallel lines p and q at a 90 degree angle, the two alternate exterior angles created are both 90 degrees. Granted the lines are parallel, the exterior angles created by the transversal will always be equal, so if the upper exterior angle is 136 degrees then the lower exterior angle will be as well. If the lines are not parallel, then the exterior angles have no particular relationship to each other.
The observation that alternate exterior angles measure equally when intercepting two parallel lines is a principle of Euclidean geometry. Euclidean geometry is the system of mathematics attributed to the Euclid, the Alexandrian Greek mathematician. His work Elements is the first known example of a sort of geometry text-book, and it approaches mathematics by deducing many different mathematical theorems from a common set of rational axioms. Besides alternate exterior angles, it also discusses three-dimensional trigonometry and precedes algebra. Apart from Euclid’s own theorems, it also contains much which had been discovered by earlier mathematicians.
As well as alternate exterior angles, observations can be made about alternate interior angles. Exactly the same phenomenon occurs with alternate interior angles when a transversal crosses two parallel lines as with the alternate exterior angles; that is, the angles created at either end of the transversal where it crosses with the parallel lines are congruent. Likewise, when the two lines that are being crossed by the transversal are not parallel, there will be seemingly no relationship between the alternate interior angles. The distinction is that whilst exterior angles means angles created outside the lines, interior angles means angles created inside the lines.
This relationship between the alternate exterior angles created when a transversal crosses two parallel lines is explained in one of the eight geometrical theorems which concern transversals. These theorems are numbered 9-16, and besides the theorem about alternate exterior angles, also include the relationship explained above regarding alternate interior angles. Other relevant theorems include: the corresponding angles created when a transversal intersects two parallel lines are congruent, and the interior angles created on the same side of the transversal under the same circumstances are supplementary. The latter four theorems in this set converses of this first set of four.